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Stochastic Ruminations: Is Modeling in Your Future?
We build models for a variety of reasons, including:
- to gain a better understanding of a process, structure, or
operation
- to identify how a change might affect the real world by
observing changes in the model.
- to predict a future behavior based on a priori data
Consider the classic problem of fitting the piano in the right
place in the living room. An appropriate model may be a scale
drawing or even a three-dimensional prototype of the room and all
its furniture. It's a lot easier to move the paper or cardboard
piano than the real thing.
While models can be constructed in many different ways,
mathematical models are efficient tools for decision-making
processes. In one project,
the manager of a manufacturing plant was insistent on needing a
significant capital investment for a new piece of equipment. The
CFO questioned why he needed yet another one when he already had
ten and the overall demand had not changed significantly.
While the overall demand had not changed, the demand patterns
had changed dramatically. The plant manager argued that this would
require additional machine setups during each shift in order to accommodate
the change. As the setups were time-consuming, they reduced both
throughput and efficiency.
Enter the mathematical model: we developed a set of equations
that described the production time required to process the daily
demand. The total production time to meet the daily demand
exceeded the 10 machine-days due to the large setup time between
major product lines. Then we adjusted the model to try alternate
configurations. Using linear programming techniques, we varied the
configuration parameters and solved multiple simultaneous equations
to maximize throughput.
The result is that the plant manager can meet the
demand requirements with the existing equipment by pre-configuring
certain machines for specific product lines. It was a lot easier
to use a mathematical
model than to change configurations and experiment in a trial
and error fashion.
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